Numerical Analysis of Turbulent Flow in a Rectangular Duct with Periodic Arrays of Blocks

Abstract

Numerical analysis has been performed for three-dimensional developing turbulent flow in a rectangular cross sectioned duct with periodic arrays of blocks by using an algebraic Reynolds stress model. Upper and bottom wall of straight duct with rectangular cross section are composed of many blocks, which are periodically located along the flow direction. In the numerical calculation, periodic boundary condition has been used for this flow and an algebraic Reynolds stress model is adopted in order to predict precisely Reynolds stresses. Since the presented algebraic stress model is classified into high Reynolds number turbulent model, wall function method has to be used to set boundary condition of turbulent energy and dissipation. As for this wall function method, we have examined the influence of universal constant which appears in log-law velocity profile by means of changing its value. We have adopted two kinds of universal constants, that is, one is the value with 5.5 for smooth wall and the other is -8.0 for roughened wall. Each calculated result of mean velocity and Reynolds stresses is compared with the experimental data. As the result of this research, it has been found that calculated results for universal constant-8.0 have shown the reasonable result compared with the calculated results for universal constant 5.5. Besides, calculated results of Reynolds stresses for -8.0 are in better agreement with the experimental results than that for 5.5. The calculated results of secondary flow have suggested that flow behavior near wall flow depends on universal constant in log-law velocity profile. These calculated results indicate that the universal constant of log-law velocity which is assumed in wall function, has to be changed according to the wall condition.